A sum of Rs. 8,000 is invested for 2 years at 10% per annum compound interest. Calculate :
final amount at the end of the second year.

Answer

To calculate the final amount at the end of the second year for a sum of Rs. 8,000 invested at a compound interest rate of 10% per annum for 2 years, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Principal (P) = Rs. 8,000
- Rate of Interest (R) = 10% per annum
- Time (n) = 2 years

2. **Use the Compound Interest Formula**:
The formula for calculating the amount (A) using compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]

3. **Substitute the Values into the Formula**:
Substitute the values of P, R, and n into the formula:
\[ A = 8000 \left(1 + \frac{10}{100}\right)^2 \]

4. **Simplify the Expression Inside the Parentheses**:
Calculate \(1 + \frac{10}{100}\):
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]

5. **Raise the Result to the Power of n**:
Now, raise 1.1 to the power of 2:
\[ (1.1)^2 = 1.1 \times 1.1 = 1.21 \]

6. **Calculate the Final Amount**:
Now multiply the principal by the result from the previous step:
\[ A = 8000 \times 1.21 = 9680 \]

7. **Final Result**:
Therefore, the final amount at the end of the second year is:
\[ A = Rs. 9,680 \]

### Summary:
The final amount at the end of the second year is Rs. 9,680.

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